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# Lecture23222

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### Lecture23222

1. 1. Kinetics: Integrated Rate Laws Lecture 23
2. 2. Integrated rate laws
3. 3. A sample problem on determining reactant concentration at a given time.
4. 4. If we obtain a straight line, <ul><li>when we plot ln[reactant] vs time, the reaction is first order with respect to that reactant. </li></ul><ul><li>when we plot 1/ [reactant] vs time, the reaction is second order with respect to that reactant. </li></ul><ul><li>when we plot [reactant] vs time, the reaction is zero order with respect to that reactant. </li></ul>
5. 5. Graphical determination of the reaction order: look for a straight line
6. 6. The half-life (t 1/2 ) of a reaction is the time required for the reactant concentration to reach half of its initial value.
7. 7. The half-life of a first order reaction <ul><li>ln([A] 0 /[A] t )=kt </li></ul><ul><li>ln([A] 0 /0.5[A] 0 )=kt 1/2 </li></ul><ul><li>ln2=kt 1/2 , 0.693=kt 1/2 </li></ul><ul><li>t 1/2 = ln2/k = 0.693/k </li></ul>
8. 8. Half-life in a first order process
9. 9. In the radioactive decay of elements, decomposition of each particle in a first order process is independent of the number of particles.
10. 10. The half-life of a second order reaction <ul><li>1/[A] t — 1/[A 0 ] = kt </li></ul><ul><li>1/0.5[A] 0 — 1/[A 0 ] = kt 1/2 </li></ul><ul><li>2/[A] 0 — 1/[A 0 ] = kt 1/2 </li></ul><ul><li>1/[A 0 ] = kt 1/2 </li></ul><ul><li>t 1/2 =1/k[A 0 ] </li></ul>
11. 11. Half-life in a second order process
12. 12. The half-life of a zero order reaction <ul><li>[A] t — [A] 0 = — kt </li></ul><ul><li>0.5[A] 0 — [A 0 ] = — kt 1/2 </li></ul><ul><li>— 0.5[A] 0 = — kt 1/2 </li></ul><ul><li>0.5[A] 0 = kt 1/2 </li></ul><ul><li>[A] 0 = 2kt 1/2 </li></ul><ul><li>t 1/2 = [A] 0 /2k </li></ul>
13. 13. Half-life in a zero order process
14. 14. The half-life and reaction order <ul><li>The half-life of a first-order reaction is a constant, independent of reactant concentration. </li></ul><ul><li>The half-life of a second-order reaction is inversely proportional to the initial reactant concentration. </li></ul><ul><li>The half-life of a zero-order reaction is directly proportional to the initial reactant concentration. </li></ul>
15. 15. A sample problem on determining the half-life of a first-order reaction.
16. 16. THE END